An application of binomial coefficients to social choice theory. (English) Zbl 1290.11036
Summary: In this paper we determine the number of positive integer sequences \(a_1,a_2,\ldots,a_k\) such that \(1\leq a_1\leq \cdots \leq a_k \leq m\) and \(a_i\geq i\) for all \(i\in \{1,\ldots, k\}\). After that, we apply this result to calculate the number of anonymous, neutral and monotonic social welfare functions when only two alternatives are considered.
MSC:
11B65 | Binomial coefficients; factorials; \(q\)-identities |
91B12 | Voting theory |
91B14 | Social choice |